Detailed examination of damaged nails, say (8)
I believe the answer is:
analysis
'detailed examination' is the definition.
(I've seen this before)
'damaged nails say' is the wordplay.
'damaged' indicates an anagram.
'nails'+'say'='nailssay'
'nailssay' anagrammed gives 'ANALYSIS'.
'of' acts as a link.
(Other definitions for analysis that I've seen before include "Study of mind" , "Examination of structure of problem" , "Dissection and examination" , "Determination" , "Detailed interpretation" .)